Yet another thing easier in fanfic than in canon: pick up your favorite characters, put them in a different setting, time, or planet, and see what happens. Yes, Hercules: TLJ pulled this one off too. The actors playing characters in the French Revolution will never not be funny. All hail the Chartreuse Fox!
Trick #3: Another Time, Another Place, Another Story.
Many, many ways there are to pull this off. Let’s see some of the classic subcategories.
The Fantasy AU. Exactly what it says on the tin; characters written into a classic fantasy world instead of the canon one. Dragons optional but definitely recommended. Knights, wizards, kitsune and shapeshifters common.
The SF AU. Ditto, but with space travel. Sometimes a generic space setting, sometimes a deliberate fusion with worlds like Star Wars, Star Trek, and the Firefly ‘verse. BTW I firmly hold that while Wei Wuxian may look like a disaster to anyone outside the Jedi Council, he’s actually one of the sanest and best they have. While Lan Wangji is one bad day away from being a Sith. All those attachment issues…. Escape Your Destiny is a good fic for that one.
The Superhero AU. Neither SF nor Fantasy, though it has elements of each. Superhero AUs are about characters having flashy powers, Fighting Crime, and otherwise being even more Dramatic than canon. BNHA and MCU fusion fics are common varieties; garden-variety superhero worlds abound as well.
The Time Travel AU. This is a particularly tricky one because it’s also often a Fix-It Fic. Nothing wrong with that, it’s just often a lot of plot is one character desperately trying to set right what in canon went wrong; sometimes with better results than others. This more than the other varieties relies on canon as a backdrop. The characters have to know what they’re trying to fix!
Some stories do mix it up with a side character who doesn’t know half of what really went wrong. Meaning you get the readers on the edge of their seats, trying to guess what will get fixed and what will be missed with horrible consequences….
Finally, you have various flavors of Modern AU. This can range from “characters in a completely normal life” (coffee-shop AUs, high school) to “characters think they’re in a normal life, but there’s actually going to be an unexpected genre shift to Urban Fantasy, Zombie Apocalypse, or Alien Invasion inside three pages”.
Canon provides a background for all these fanfic variants to play out, adding color and substance far beyond what your own wordcount would let you pull off. It lets everyone spin countless variants on a theme; much like the myriad King Arthur stories written centuries ago drew on the central “knights of the Round Table” concept everybody had heard of. Note, I’m not sure anyone back then wrote King Arthur IN SPACE… but I wouldn’t be at all surprised!
Crossover Queen's Creative Chaos 
The best part about the AUs is that they never quite fit the characters as-is.
And exactly where the author chooses to make tiny adjustments can cast things in an entirely different way.
That petty bully is now a noble… which makes his bullying have more implications than just pettiness.
That poor street rat is now in a society with universal literacy, which means even a street rat can read that [do not touch] label.
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I’m suddenly quite sure that a lot of people wrote Charlemagne in Space!!! stories, they just weren’t very obvious about it.
Helped by it not being as immediately noticeable as, oh, Seven Samurai or Journey to the West.
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If you want a show that does similar things in canon check out Tsubasa reservoir chronicle. It’s very fun
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